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Homological mirror symmetry for Calabi-Yau hypersurfaces in projective space. (English) Zbl 1344.53073
This review is based on the abstract of the paper:
Its objective is to prove the Homological Mirror Symmetry for a smooth $$d$$-dimensional Calabi-Yau hypersurface in projective space for any $$d\geq 3$$. The main ingredients for the the proof are the following:
(1)
The construction of an immersed Lagrangian sphere in a $$d$$-dimensional pair of pants.
(2)
The introduction of the relative Fukaya category and an understanding of its grading structure.
(3)
A description of the behaviour of this category with respect to branched covers via an orbifold Fukaya category.
(4)
A Morse-Bott model for the relative Fukaya category that allows one to make explicit computations.
(5)
The introduction of certain graded categories of matrix factorizations mirror to the relative Fukaya category.

##### MSC:
 53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category 14J33 Mirror symmetry (algebro-geometric aspects)
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##### References:
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